Orthogonal Frequency Division Multiplexing (OFDM) is a widely used technique for achieving high data rate and combating multipath fading in wireless communications. In OFDM, all the orthogonal carriers are transmitted simultaneously wherein the entire allocated bandwidth is occupied through the aggregated sum of the narrow orthogonal subcarriers. By transmitting several symbols at the same time, the effective symbol duration is increased commensurately. As a consequence, the effects of ISI caused by dispersive Rayleigh fading environment is reduced.
Currently, there are three approved standards of Wireless Local Access Networks (WLAN) that utilize OFDM for their physical layer specifications. They are the High Performance Local Area Network (Type 2) (HiperLAN/2), Mobile Multimedia Access Communications (MMAC) and the IEEE 802.11a. Each standard offers data rates ranging from 6 Mbps to 54 Mbps. The packet preamble specified by the IEEE 802.11a standard consists of ten identical short and two identical long OFDM training symbols where t1 to t10 denote the short training symbols (each containing 16 samples) and T1 and T2 denote the long training symbols (each containing 64 samples). The short and long preamble symbols are followed by a signal field which in turn is followed by the data field. The structure of the WLAN preamble enables the receiver to use a very simple and efficient algorithm to detect it. Since the time-domain short and long training sequences are periodic, a delay and correlate type of algorithm can be used. The 802.11a standard uses a sixteen sample delay line and a conjugator so that the incoming samples in each short training symbol, t1-t10, is correlated with the samples in the same position in the previous short training symbol. The conjugate of the delayed samples and the present incoming samples are multiplied together and a moving average is determined. The moving average output, which will be a real number if there is a perfect match and will be a complex number including an imaginary term, if, as more normally, there is a mismatch, is submitted to a magnitude squarer and delivered to a divider. The delayed samples are also submitted to a magnitude squarer after which a moving average is determined and is squared before also being submitted to the divider to normalize the output of the divider so that the matching will be independent of the input signal intensity. The output of the divider is then submitted to a threshold unit such as a comparator. If it exceeds a predefined threshold, a match is indicated. While the approach works well, it has some shortcomings: the square of the absolute value of a complex number and the square of a real number have to be calculated. One operation would require two multiplications and one addition, the other, one multiplication in addition to the divider operation. This results in complex circuits which require significant power.